As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.In this manuscript, we examine the role of image charge effects on the electrostatic potential fluctuations experienced by ionic species in the vicinity of an electrode surface. We combine simulation and theory to quantify these fluctuations and how they vary with distance from the electrode surface. We observe that the potential distribution narrows significantly for species within a few electrolyte screening lengths of the electrode. We attribute this narrowing to the effects of image charge fluctuations originating from the polarization response of the electrode. We show that the physical consequences of these image charge effects can be captured in the context of a simple analytical field theory with anti-symmetric boundary conditions. We contextualize these results by discussing their implications for rates of Marcus-like outer-sphere interfacial electron transfer.The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.We present two multistate ring polymer instanton (RPI) formulations, both obtained from an exact path integral representation of the quantum canonical partition function for multistate systems. The two RPIs differ in their treatment of the electronic degrees of freedom; while the Mean-Field (MF)-RPI averages over the electronic state contributions, the Mapping Variable (MV)-RPI employs explicit continuous Cartesian variables to represent the electronic states. We compute both RPIs for a series of model two-state systems coupled to a single nuclear mode with electronic coupling values chosen to describe dynamics in both adiabatic and nonadiabatic regimes. We show that the MF-RPIs for symmetric systems are in good agreement with the previous literature, and we show that our numerical techniques are robust for systems with non-zero driving force. The nuclear MF-RPI and the nuclear MV-RPI are similar, but the MV-RPI uniquely reports on the changes in the electronic state populations along the instanton path. In both cases, we analytically demonstrate the existence of a zero-mode, and we numerically find that these solutions are true instantons with a single unstable mode as expected for a first order saddle point. Finally, we use the MF-RPI to accurately calculate rate constants for adiabatic and nonadiabatic model systems with the coupling strength varying over three orders of magnitude.We present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green's function theory in the GW approximation with the Bethe-Salpeter equation (BSE). This work provides a summary of the underlying theory and discusses the details of its implementation based on Gaussian orbitals, including resolution-of-identity techniques and different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using graphics processing units in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA-XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on an atomistic level in a coupled quantum- and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW-BSE implementation are illustrated with two examples. First, we study the dependence of optically active electron-hole excitations in a series of diketopyrrolopyrrole-based oligomers on molecular-architecture modifications and the number of repeat units. Second, we use the GW-BSE/MM setup to investigate the effect of polarization on localized and intermolecular charge-transfer excited states in morphologies of low-donor content rubrene-fullerene mixtures. https://www.selleckchem.com/products/fezolinetant.html These showcases demonstrate that our implementation currently allows us to treat systems with up to 2500 basis functions on regular shared-memory workstations, providing accurate descriptions of quasiparticle and coupled electron-hole excited states of various characters on an equal footing.In a previous paper [M. Dittner and B. Hartke, J. Chem. Theory Comput. 14, 3547 (2018)], we introduced a preliminary version of our GOCAT (globally optimal catalyst) concept in which electrostatic catalysts are designed for arbitrary reactions by global optimization of distributed point charges that surround the reaction. In this first version, a pre-defined reaction path was kept fixed. This unrealistic assumption allowed for only small catalytic effects. In the present work, we extend our GOCAT framework by a sophisticated and robust on-the-fly reaction path optimization, plus further concomitant algorithm adaptions. This allows smaller and larger excursions from a pre-defined reaction path under the influence of the GOCAT point-charge surrounding, all the way to drastic mechanistic changes. In contrast to the restricted first GOCAT version, this new version is able to address real-life catalysis. We demonstrate this by applying it to the electrostatic catalysis of a prototypical Diels-Alder reaction. Without using any prior information, this procedure re-discovers theoretically and experimentally established features of electrostatic catalysis of this very reaction, including a field-dependent transition from the synchronous, concerted textbook mechanism to a zwitterionic two-step mechanism, and diastereomeric discrimination by suitable electric field components.